Relative Permeability Scaling From Pore-Scale Flow Regimes

Relative permeability measurements are commonly fitted with the Corey and Brooks-Corey correlations. Despite such correlations fit experimental data generally well, they are mostly of an empirical nature. Here, we propose a semiempirical model to determine relative permeabilities of the wetting and the nonwetting phases in real 3-D porous media that accounts for pore-scale flow regimes. The starting point is the homogenization framework proposed by Picchi and Battiato (2018, https:// doi .org/10.1029/ 2018WR023172), where the upscaling is conducted for different spatial distributions of the flowing phases in the capillary tube setting. First, we extend the approach to realistic media by allowing pore-scale flow regimes to coexist in a complex geometry while accounting for capillary and viscous limits in the dynamics. Then, we discuss the scaling behavior of normalized relative permeabilities in terms of the phases viscosity ratio and identify three classes which govern their scaling. We also derive an analytical expression for the fractional flow. Finally, we provide a detailed validation of the proposed model for both relative permeabilities and fractional flow against data from numerical simulations and experiments available in the literature. The data set used for validation covers a wide range of systems, ranging from brine-CO2 to oil-water flows. The equations derived capture well the trend of both numerical and experimental data.